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Proof step 7 from proof insperm-01 (previous step)

perm(a ' + y, ins≤(a, y)), perm(a ' + x, ins≤(a, x)), perm(ins≤(a, x), a ' + x), perm(ins≤(a, y), a ' + y) ⊦ perm(ins≤(a, x), ins≤(a, y)) ↔ perm(x, y)

User applied rule case distinction

And obtained the following new goals

Proof step 8:
perm(x, y), perm(a ' + y, ins≤(a, y)), perm(a ' + x, ins≤(a, x)), perm(ins≤(a, x), a ' + x), perm(ins≤(a, y), a ' + y) ⊦ perm(ins≤(a, x), ins≤(a, y))

Rule argument

pos: right 1

Additional information

Used simplifier rules: trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z); (forward) from specification list-perm%sym-01: ⊦ perm(x, y) → perm(y, x); (forward) from specification list-perm%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x); (forward) from specification list-perm%app: ⊦ perm(x + y, x + z) ↔ perm(y, z); from specification list-perm%a: ⊦ (x + y) + z = x + y + z; from specification list